Lattice model (mathematics)

In geometry and group theory, a lattice in ${\displaystyle \mathbb {R} ^{n}}$ is a subgroup of the additive group ${\displaystyle \mathbb {R} ^{n}}$ which is isomorphic to the additive group ${\displaystyle \mathbb {Z} ^{n}}$, and which spans the real vector space ${\displaystyle \mathbb {R} ^{n}}$. In other words, for any basis of ${\displaystyle \mathbb {R} ^{n}}$, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice. A lattice may be viewed as a regular tiling of a space by a primitive cell.

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